FREE VIBRATION ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES EMBEDDED IN AN ELASTIC MEDIUM USING DTM (DIFFERENTIAL TRANSFORMATION METHOD)

Abstract

The study of vibration in carbon nanotubes (CNTs) is currently a major topic of interest that increases understanding of their dynamic mechanical behavior. By now, there are three methods to analyze the mechanical properties of carbon nanotube (CNT). They are spectroscopy experiment, computational simulation, and theoretical analysis. However, technically these are difficult experiments of vibrational properties because of the small diameter of the nanotubes, and plenty of time will be spent on the molecular dynamics (MD) simulation. Theoretical analyses have shown the advancement of the taken cost and the spent time of researches compared with the experimental operation and molecular dynamic (MD) simulation method, and they can predict some results which cannot be achieved by the other two methods by now. Elastic continuum models are used to study the vibrational behavior of carbon nanotubes to avoid the difficulties encountered during experimental characterization of nanotubes as well as the time-consuming nature of computational atomistic simulations. To calculate the resonant vibration of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium, a theoretical analysis is presented based on Euler-Bernoulli beam model and Winkler spring model.

Keywords

• Buvnov-Galerkin
• Differential transformation method (DTM)
• Doublewalled carbon nanotubes (DWCNTs)
• MATLAB
• Petrov-Galerkin